В треугольнике со сторонами: a = 1.769, b = 2, с = 2.17, углы равны α° = 50°, β° = 60°, γ° = 70°
Ответ:
a=1.769
b=2
c=2.17
α°=50°
β°=60°
γ°=70°
S = 1.664
ha=1.881
hb=1.664
hc=1.534
P = 5.939
Решение:
Сторона:
c = b·
sin(γ°)
sin(β°)
= 2·
sin(70°)
sin(60°)
= 2·
0.9397
0.866
= 2·1.085
= 2.17
Угол:
α° = 180 - γ° - β°
= 180 - 70° - 60°
= 50°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √22 + 2.172 - 2·2·2.17·cos(50°)
= √4 + 4.709 - 8.68·0.6428
= √3.129
= 1.769
или:
a = b·
sin(α°)
sin(β°)
= 2·
sin(50°)
sin(60°)
= 2·
0.766
0.866
= 2·0.8845
= 1.769
или:
a = c·
sin(α°)
sin(γ°)
= 2.17·
sin(50°)
sin(70°)
= 2.17·
0.766
0.9397
= 2.17·0.8152
= 1.769
Периметр:
P = a + b + c
= 1.769 + 2 + 2.17
= 5.939
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√2.97·(2.97-1.769)·(2.97-2)·(2.97-2.17)
=√2.97 · 1.201 · 0.97 · 0.8
=√2.76796872
= 1.664
Высота :
ha =
2S
a
=
2 · 1.664
1.769
= 1.881
hb =
2S
b
=
2 · 1.664
2
= 1.664
hc =
2S
c
=
2 · 1.664
2.17
= 1.534